If you sign up for AA's Platinum Challenge you'd end up as AA Platinum (Oneworld Sapphire) with 32,000+ spendable miles. As your flights would be in September, your status would last until the end of February 2017.

AA Plat gets you 100% mileage bonus, Oneworld lounge access on non-US domestic flights, additional baggage allowances, free advance seat selection on BA, yadda yadda.

You'd have enough tier points for BA Silver (OW Sapphire) but BA requires 4 BA-metal segments before the status is conveyed, and you'd have none with this itinerary.